Libraries of random, inhibitory hairpin RNA and methods for constructing such libraries have important applications in identifying therapeutic RNA molecules and RNA molecules with biological activity; but the libraries have been extremely difficult to synthesize because of the limitations of conventional procedures for randomization and generation of RNA libraries. Applicants have provided the foregoing as described in U.S. Published Application No. 2009-0285788, which is hereby incorporated by reference in its entirety. Random mutagenesis on hit sequences from one of the foregoing libraries to improve them, and an improved sequence had a key mismatch, and it was shown that that mismatch per se contributed to potency (Wang et al., PLoS ONE 3: e3171, 2008). In addition, endogenous miRNAs almost invariably have mismatches. There exists a further long-standing need in the art for methods of constructing random, inhibitory hairpin RNA libraries where the random duplex RNA itself contains random mismatches. Such libraries have important applications in identifying therapeutic RNA molecules and RNA molecules with biological activity, but are even more difficult to synthesize because of the limitations of conventional procedures for their generation.